Momentum, energy and charge are conserved in all nuclear reactions - Leaving Cert Physics - Question (a) - 2018

$n \rightarrow p + e^- + \bar{ U}$

Pauli believed the neutrino could not be detected because it has:

• No charge: Being neutral, it does not interact electromagnetically.
• Very small mass: Its mass is so tiny that it hardly interacts with other matter, making detection extremely challenging.

Two gamma-ray photons are produced to conserve momentum during the pair annihilation process. When an electron and positron collide, their combined momentum is converted into the momentum of the resulting photons, ensuring that total momentum before and after the annihilation remains equal.

Charge is conserved because the electron and positron have equal and opposite charges. Before the annihilation, the total charge is zero (since the positron has a +1 charge and the electron has a -1 charge). After annihilation, the resultant photons have no charge, maintaining the balance.

Using the equation for energy, we have:

$E = mc^2$

For each photon, we also use:

$E = hf$

Equating these, we find:

$f = \frac{E}{h} = \frac{mc^2}{h}$

Substituting the mass-energy of the positron (and electron) gives:

$f = \frac{1.24 \times 10^{-20}}{h}$

This results in:

$f = 1.24 \times 10^{20}\ ext{ Hz}$

The two other negatively charged leptons are the muon and the tau.

The three forces are:

1. Electromagnetic
2. Weak
3. Gravitational